How can you relief pain in these areas after martial arts training?

Stretching. It is important to stretch prior to workouts, but moreso after your workout session. Take advantage of the muscles being warm to slowly elongate and relax them after the workout.
What areas? I'll try to answer your question, based on my own injuries in martial arts training. For general aches/bruises after training, the best thing is a cold compress. Apply for 20 min over the bruise to not only reduce pain, but reduce swelling/bleeding in the injured tissue. Avoid aspirin/aspirin containing products. Massage can help relieve pain, along with topical pain relievers.